The particle's position as a funciton of time is given as `x=5t^2-9t+3`. Find out the maximum value of position co-ordinate? Also, plot the graph.

Explanation

We are given `x=5t^2-9t+3`, the position is changing with x.
Differentiate x w.r.t t, we get `(dx)/(dt)=10t-9=0`
`:. t=9//10=0.9`
Check whether maxima or minima exists.
We need to do double differentiation test: `(d^2x)/(dt^2)=10gt0`
Therefore, there exists a minima at `t=0.9`
Now, check for the limiting values.
When `t=0`, `x=3` and when `t=oo`, `x=oo`.
So, the maximum position co-ordinate does not exist.